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Question
If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.
Options
3
6
9
1
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Solution
If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to 9.
Explanation:
Since x = `int_0^y "dt"/sqrt(1 + 9"t"^2)`
⇒ `"dx"/"dy" = 1/sqrt(1 + 9y^2)`
which gives `("d"^2y)/("dx"^2) = (18y)/(2sqrt(1 + 9y^2)) * "dy"/"dx"`
= 9y.
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